International Journal of Optimization in Civil Engineering
Volume:14 Issue: 3, Summer 2024

Spillway design poses a significant challenge in effectively managing the energy within water flow to prevent erosion and destabilization of dam structures. Traditional approaches typically advocate for standard hydraulic jump stilling basins or other energy dissipators at spillway bases yet constructing such basins can be prohibitively large and costly, particularly when extensive excavation is necessary. Consequently, growing interest in cascade hydraulic structures has emerged over recent decades as an alternative for energy dissipation. These structures utilize a series of arranged steps to facilitate water flow, effectively dissipating energy as it traverses the cascade. Commonly deployed in scenarios involving high dams or steep gradients, the stepped configuration ensures efficient aeration and substantial energy dissipation along the structure, thereby reducing the size and cost of required stilling basins. Despite extensive research on hydraulic characteristics using physical and numerical models and established design procedures, construction cost optimization of step cascades remains limited but promising. This paper aims to address this gap by employing two novel gradient-based meta-heuristic optimization techniques to enhance the efficiency and cost-effectiveness of cascade stilling basin designs. Through comparative analyses and evaluations, this study demonstrates the efficacy of these techniques and offers insights for future research and applications in hydraulic structures design optimization.

In order to evaluate the damage state, value, and position of structural members more accurately, a multi-objective optimization (MO) method is utilized that is based on changes in natural frequency. The multi-objective optimization dynamic-based damage detection method is first introduced. Two objective functions for optimization are then introduced in terms of changing the natural frequencies and mode shapes. The multi-objective optimization problem (MOP) is formulated by using the two objective functions. Three considered MO algorithms consist of Colliding Bodies Optimization (MOCBO), Particle Swarm Optimization (MOPSO), and non-dominated sorting genetic algorithm (NSGA-II) to achieve the best structural damage detection. The proposed methods are then applied to three planar steel frame structures. Compared to the traditional optimization methods utilizing the single-objective optimization (SO) algorithms, the presented methods provide superior results.

The optimal design of structural systems represents a pivotal challenge, striking a balance between economic efficiency and safety. There has been a great challenge in balancing between the economic issues and safety factors of the structures over the past few decades; however, development of high-speed computing systems enables the experts to deal with higher computational efforts in designing structural systems. Recent advancements in computational methods have significantly improved our ability to address this challenge through sophisticated design schemes. The main purpose of this paper is to develop an intelligent design scheme for truss structures in which an optimization process is implemented into this scheme to help the process reach lower weights for the structures. For this purpose, the Artificial Rabbits Optimization (ARO) algorithm is utilized as one of the recently developed metaheuristic algorithms which mimics the foraging behaviour of the rabbits in nature. In order to reach better solutions, the improved version of this algorithm is proposed as I-ARO in which the well-known random initialization process is substituted by the Diagonal Linear Uniform (DLU) initialization procedure. For numerical investigations, 5 truss structures 10, 25, 52, 72, and 160 elements are considered in which stress and displacement constraints are determined by considering discrete design variables. By conducting 50 optimization runs for each truss structure, it can be concluded that the I-ARO algorithm is capable of reaching better solutions than the standard ARO algorithm which demonstrates the effects of DLU in enhancing this algorithm’s search behaviour.

The sine-cosine algorithm is concerned as a recent meta-heuristic method that takes benefit of orthogonal functions to scale its walking steps through the search space. The idea is utilized here in a different manner to develop a modified sine-cosine algorithm (MSCA). It is based on the controlled perturbation about current solutions by applying a novel combination of sine and cosine functions. The desired transition from exploration to exploitation phases mainly relies on such a term that provides continued fluctuations within a dynamic amplitude. Performance of the proposed algorithm is further evaluated on a set of thirteen test functions with unimodal and multimodal search spaces, as well as on engineering and structural problems in a variety of discrete, continuous and mixed discrete-continuous types. Numerical simulations show that MSCA can find the best literature results for such benchmarks problems. Additional fair comparisons, declare competitive performance of the proposed method with other meta-heuristic algorithms and its enhancement with respect to the standard sine-cosine algorithm.

The contourlet transform as an extension of the wavelet transform in two dimensions uses the multiscale and directional filter banks, and has a more adequate performance in comparison with the classical multi-scale representations. In this study, the efficiency of the contourlet transform is assessed for identifying the damage of plate structures in various conditions. The conditions include single damage and multi–damages with different shapes and severities, the different supports (i.e., boundary conditions), and the higher mode shapes,. For achieving this purpose, the process of the damage detection of plate structures using contourlet transform is implemented in the three steps. In the first step, the first mode shapes of a damaged plate and a reference state as the intact plate are obtained using the finite element method. In the second step, the damage indices are achieved by applying the contourlet transform to the responses of the first mode shapes for the damaged and intact plates. Finally, the location and the approximate shape of the damage are identified by plotting the damage indices. The obtained results indicate that the various conditions influence the performance of the contourlet transform for identifying the location and approximate shape of damages in plate structures.